[/quote]

Yea thats definitely a faulty PSU, especially if all Apollos are running fine with a bigger PSU, and the fault happens even when you switch different Apollo units.

450 W PSU should not be tripping with a 150W load.
[/quote]

I think the chances were 99:1 that I had bought a faulty PSU due to its behaviour after swapping all the boxes from the suspicious PSU to the bigger one I had, yes.

...BUT

[/quote]
I recall older ATX power supplies required some load (something in the 1A range) also on the 5V rail in order to keep the 12V rail stable. That may still apply to cheaper power supply models.
[/quote]

...I plugged to the SATA line the only thing I had at hand, i.e. a small SSD drive,  that pulls exactly  5V 1A.
And it worked!! AWESOME, the 3rd Apollo has been mining and stable for one odd hour (vs. shutting off power after a few seconds or just one minute) and I think that this smart little trick solves the issue very nicely.

The bottom line - beware of cheap non-modular PSUs but if you use one keep it "alive" by plugging something to the 5V rail.
Now I am thinking  what can I add to this set (I need to keep my SSD) for my friend so to make the whole thing work. Maybe a fancy USB gadget like a mini-vacuum cleaner or a few USB fans would do, plus a SATA to USB adapter cable of course - any ideas?

Ah, @philipma1957, thanks for the links to better PSUs, the modular ones around 500-650w are my personal bet for powering up bundles of 2-3 Apollos if I buy a few more of them.

Again , thanks to everybody for your very helpful insight.